This higher order function "mapList" can be used in a wide range of areas to simplify code.

It is called

map

in Haskell's Prelude.

2.1.3 Mathematical examples

In mathematics the counterpart to higher order functions are functionals (mapping functions to scalars) and function operators (mapping functions to functions).
Typical functionals are the limit of a sequence, or the integral of an interval of a function.